mgwr.sel_bw.Sel_BW¶

class mgwr.sel_bw.Sel_BW(coords, y, X_loc, X_glob=None, family=<spglm.family.Gaussian object>, offset=None, kernel='bisquare', fixed=False, multi=False, constant=True, spherical=False)[source]¶

Select bandwidth for kernel

Methods: p211 - p213, bandwidth selection Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically weighted regression: the analysis of spatially varying relationships.

Parameters:

Parameters:	y : array n1, dependent variable. X_glob* : array nk1, fixed independent variable. X_loc* : array nk2, local independent variable, including constant. coords* : list of tuples (x,y) of points used in bandwidth selection family : string GWR model type: ‘Gaussian’, ‘logistic, ‘Poisson’‘ offset : array n1, the offset variable at the ith location. For Poisson model this term is often the size of the population at risk or the expected size of the outcome in spatial epidemiology Default is None where Ni becomes 1.0 for all locations kernel* : string kernel function: ‘gaussian’, ‘bisquare’, ‘exponetial’ fixed : boolean True for fixed bandwidth and False for adaptive (NN) multi : True for multiple (covaraite-specific) bandwidths False for a traditional (same for all covariates) bandwdith; defualt is False. constant : boolean True to include intercept (default) in model and False to exclude intercept. spherical : boolean True for shperical coordinates (long-lat), False for projected coordinates (defalut).

y : array: n*1, dependent variable.
X_glob : array: n*k1, fixed independent variable.
X_loc : array: n*k2, local independent variable, including constant.
coords : list of tuples: (x,y) of points used in bandwidth selection
family : string: GWR model type: ‘Gaussian’, ‘logistic, ‘Poisson’‘
offset : array: n*1, the offset variable at the ith location. For Poisson model this term is often the size of the population at risk or the expected size of the outcome in spatial epidemiology Default is None where Ni becomes 1.0 for all locations
kernel : string: kernel function: ‘gaussian’, ‘bisquare’, ‘exponetial’
fixed : boolean: True for fixed bandwidth and False for adaptive (NN)
multi : True for multiple (covaraite-specific) bandwidths: False for a traditional (same for all covariates) bandwdith; defualt is False.
constant : boolean: True to include intercept (default) in model and False to exclude intercept.
spherical : boolean: True for shperical coordinates (long-lat), False for projected coordinates (defalut).

Examples

>>> import libpysal as ps
>>> from mgwr.sel_bw import Sel_BW
>>> data = ps.io.open(ps.examples.get_path('GData_utm.csv'))
>>> coords = list(zip(data.by_col('X'), data.by_col('Y')))
>>> y = np.array(data.by_col('PctBach')).reshape((-1,1))
>>> rural = np.array(data.by_col('PctRural')).reshape((-1,1))
>>> pov = np.array(data.by_col('PctPov')).reshape((-1,1))
>>> african_amer = np.array(data.by_col('PctBlack')).reshape((-1,1))
>>> X = np.hstack([rural, pov, african_amer])

Golden section search AICc - adaptive bisquare

>>> bw = Sel_BW(coords, y, X).search(criterion='AICc')
>>> print(bw)
93.0

Golden section search AIC - adaptive Gaussian

>>> bw = Sel_BW(coords, y, X, kernel='gaussian').search(criterion='AIC')
>>> print(bw)
50.0

Golden section search BIC - adaptive Gaussian

>>> bw = Sel_BW(coords, y, X, kernel='gaussian').search(criterion='BIC')
>>> print(bw)
62.0

Golden section search CV - adaptive Gaussian

>>> bw = Sel_BW(coords, y, X, kernel='gaussian').search(criterion='CV')
>>> print(bw)
68.0

Interval AICc - fixed bisquare

>>> sel = Sel_BW(coords, y, X, fixed=True)
>>> bw = sel.search(search_method='interval', bw_min=211001.0, bw_max=211035.0, interval=2)
>>> print(bw)
211025.0

Attributes:

Attributes:	y : array n1, dependent variable. X_glob* : array nk1, fixed independent variable. X_loc* : array nk2, local independent variable, including constant. coords* : list of tuples (x,y) of points used in bandwidth selection family : string GWR model type: ‘Gaussian’, ‘logistic, ‘Poisson’‘ kernel : string type of kernel used and wether fixed or adaptive fixed : boolean True for fixed bandwidth and False for adaptive (NN) criterion : string bw selection criterion: ‘AICc’, ‘AIC’, ‘BIC’, ‘CV’ search_method : string bw search method: ‘golden’, ‘interval’ bw_min : float min value used in bandwidth search bw_max : float max value used in bandwidth search interval : float interval increment used in interval search tol : float tolerance used to determine convergence max_iter : integer max interations if no convergence to tol multi : True for multiple (covaraite-specific) bandwidths False for a traditional (same for all covariates) bandwdith; defualt is False. constant : boolean True to include intercept (default) in model and False to exclude intercept. offset : array n1, the offset variable at the ith location. For Poisson model this term is often the size of the population at risk or the expected size of the outcome in spatial epidemiology Default is None where Ni becomes 1.0 for all locations dmat* : array nn, distance matrix between calibration locations used to compute weight matrix sorted_dmat* : array nn, sorted distance matrix between calibration locations used to compute weight matrix. Will be None for fixed bandwidths spherical* : boolean True for shperical coordinates (long-lat), False for projected coordinates (defalut). search_params : dict stores search arguments int_score : boolan True if adaptive bandwidth is being used and bandwdith selection should be discrete. False if fixed bandwidth is being used and bandwidth does not have to be discrete. bw : scalar or array-like Derived optimal bandwidth(s). Will be a scalar for GWR (multi=False) and a list of scalars for MGWR (multi=True) with one bandwidth for each covariate. S : array nn, hat matrix derived from the iterative backfitting algorthim for MGWR during bandwidth selection R : array nnk, partial hat matrices derived from the iterative backfitting algoruthm for MGWR during bandwidth selection. There is one nn matrix for each of the k covariates. params : array n*k, calibrated parameter estimates for MGWR based on the iterative backfitting algorithm - computed and saved here to avoid having to do it again in the MGWR object.

y : array: n*1, dependent variable.
X_glob : array: n*k1, fixed independent variable.
X_loc : array: n*k2, local independent variable, including constant.
coords : list of tuples: (x,y) of points used in bandwidth selection
family : string: GWR model type: ‘Gaussian’, ‘logistic, ‘Poisson’‘
kernel : string: type of kernel used and wether fixed or adaptive
fixed : boolean: True for fixed bandwidth and False for adaptive (NN)
criterion : string: bw selection criterion: ‘AICc’, ‘AIC’, ‘BIC’, ‘CV’
search_method : string: bw search method: ‘golden’, ‘interval’
bw_min : float: min value used in bandwidth search
bw_max : float: max value used in bandwidth search
interval : float: interval increment used in interval search
tol : float: tolerance used to determine convergence
max_iter : integer: max interations if no convergence to tol
multi : True for multiple (covaraite-specific) bandwidths: False for a traditional (same for all covariates) bandwdith; defualt is False.
constant : boolean: True to include intercept (default) in model and False to exclude intercept.
offset : array: n*1, the offset variable at the ith location. For Poisson model this term is often the size of the population at risk or the expected size of the outcome in spatial epidemiology Default is None where Ni becomes 1.0 for all locations
dmat : array: n*n, distance matrix between calibration locations used to compute weight matrix
sorted_dmat : array: n*n, sorted distance matrix between calibration locations used to compute weight matrix. Will be None for fixed bandwidths
spherical : boolean: True for shperical coordinates (long-lat), False for projected coordinates (defalut).
search_params : dict: stores search arguments
int_score : boolan: True if adaptive bandwidth is being used and bandwdith selection should be discrete. False if fixed bandwidth is being used and bandwidth does not have to be discrete.
bw : scalar or array-like: Derived optimal bandwidth(s). Will be a scalar for GWR (multi=False) and a list of scalars for MGWR (multi=True) with one bandwidth for each covariate.
S : array: n*n, hat matrix derived from the iterative backfitting algorthim for MGWR during bandwidth selection
R : array: n*n*k, partial hat matrices derived from the iterative backfitting algoruthm for MGWR during bandwidth selection. There is one n*n matrix for each of the k covariates.
params : array: n*k, calibrated parameter estimates for MGWR based on the iterative backfitting algorithm - computed and saved here to avoid having to do it again in the MGWR object.

Methods

search([search_method, criterion, bw_min, …]) Method to select one unique bandwidth for a gwr model or a bandwidth vector for a mgwr model.

__init__(coords, y, X_loc, X_glob=None, family=<spglm.family.Gaussian object>, offset=None, kernel='bisquare', fixed=False, multi=False, constant=True, spherical=False)[source]¶: Initialize self. See help(type(self)) for accurate signature.